Eisenstein series for O(2,n+2)

TL;DR

This paper characterizes Eisenstein series for O(2,n+2) as Hecke eigenforms, shows their inclusion in the Maa{ ext} space, and provides explicit Fourier coefficient formulas for certain lattices.

Contribution

It introduces a new characterization of Eisenstein series for O(2,n+2) and derives explicit Fourier coefficients for even unimodular lattices.

Findings

Eisenstein series are identified as Hecke eigenforms.

Eisenstein series belong to the Maa{ ext} space.

Explicit Fourier coefficient formulas are obtained for specific lattices.

Abstract

We will characterize the Eisenstein series for O(2, n + 2) as a particular Hecke eigenform. As an application we show that it belongs to the associated Maa{\ss} space. If the underlying lattice is even and unimodular, this leads to an explicit formula of the Fourier coefficients.